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A 3 Problem 5: Rotating cylinder An infinitely long cylinder of radius R carries a uniform surface charge density R o but negligible mass density. How much work is required, per unit length, to set the cylinder spinning about its axis with angular velocity wy? Compute this in two ways and compare your answers: 0 (a) With the cylinder spinning with a time-varying angular velocity w(t), find the magnetic field and the induced electric field both inside and outside the cylinder. Find the torque per unit length required to maintain this motion in terms of Row and w and integrate to obtain the total work done per unit length as w(t) increases from 0 to ws (W = Ndo). (b) Calculate the total energy stored in the magnetic field both before and after the cylinder is spun up, and take the difference.